who gets to decide how "radical" is defined and what is classified as "radical"? I certainly agree with leaving it up to the parent.
Is antisemitism radical ? Are islamists radical ? Who knows right ? Such a tough question!
Radical means favoring extreme changes. So depending on where you live and in what part of society the things you mentioned above might not be seen as radical or they might be.
I for example would have liked to not give children access to a bible too. That might be seen as radical in some christian societies...